Question: Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{-3n^2 - 30n - 27}{2n^2 + 36n + 162}$
First factor out the greatest common factors in the numerator and in the denominator. $ y = \dfrac {-3(n^2 + 10n + 9)} {2(n^2 + 18n + 81)} $ $ y = -\dfrac{3}{2} \cdot \dfrac{n^2 + 10n + 9}{n^2 + 18n + 81} $ Next factor the numerator and denominator. $ y = - \dfrac{3}{2} \cdot \dfrac{(n + 9)(n + 1)}{(n + 9)(n + 9)}$ Assuming $n \neq -9$ , we can cancel the $n + 9$ $ y = - \dfrac{3}{2} \cdot \dfrac{n + 1}{n + 9}$ Therefore: $ y = \dfrac{ -3(n + 1)}{ 2(n + 9)}$, $n \neq -9$